Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

Details Parameters estimation for asymmetric bifurcating autoregressive processes with missing data Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

2010-12-09

arxiv.org/abs/1012.2012v3

Electronic Journal of Statistics, vol. 5 (2011) 1313-1353

Mathematics

Probability

Scientific paper

10.1214/11-EJS643

We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.

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